# Solving a Linear System in Three Variables

Solving a Linear System in Three Variables

Step 1:- Eliminate a variable. Use the elimination method to eliminate any variable from any two of the original equations. The result is an equation in two variables.

Step 2:- Eliminate the same variable again. Eliminate the same variable from any other two equations. The result is an equation in the same two variables as in Step 1.

Step 3:-  Eliminate a different variable and solve. Use the elimination method to eliminate a second variable from the two equations in two variables that result from Steps 1 and 2. The result is an equation in one variable that gives the value of that variable.

Step 4:-  Find a second value. Substitute the value of the variable found in Step 3 into either of the equations in two variables to find the value of the second variable.

Step 5 :- Find a third value. Use the values of the two variables from Steps 3 and 4 to find the value of the third variable by substituting into any of the original equations.

Step 6:-  Check the solution in all of the original equations. Then write the solution set.